A can do one-fourth of a work in 5 days and B can do two-fifth of the work in 10 days. In how many days can both A and B together do the work?

A

$$12\frac{1}{9}$$

B

$$11\frac{1}{9}$$

C

$$13\frac{1}{9}$$

D

$$10\frac{1}{9}$$